Sex differences in linear bone measurements occur following puberty but do not influence femoral or tibial torsion

Torsional, angular, and linear measurements in a paediatric population are clinically important but not well defined and understood. Different methods of measurement and discrepancies between assessors leads to a lack of understanding of what should be defined as typical or atypical for the growing skeleton. From a large dataset of 333 paediatric CT scans, we extracted three-dimensional torsional, angular, and linear measurements from the pelvis, femur, and tibia/fibula. Sex differences in linear measurements were observed in bones of children aged 13+ (around puberty), but femoral and tibial torsion were similar between males and females. The rotational profile (femoral anteversion minus tibial torsion) tended to increase with growth. Epicondylar, condylar, and malleolar widths were smaller in females than males for the same bone length after the age of 13 years, which could explain why females may be more at risk for sport injuries during adolescence. This rich dataset can be used as an atlas for researchers and clinicians to understand typical development of critical rotational profiles and linear bone measurements in children.

Bone measurements. The pelvis, femora, and tibiae/fibulae were segmented from the CT scans and meshed into a 3D surface as outlined in a previous study 20 . A template mesh for each bone was then fit to each segmented bone model, to achieve nodal correspondence between meshes. This was achieved by (1) nonrigidly registering the template model and (2) iteratively mesh fitting the template model to the segmented data using radial basis functions 20 . Bones were aligned to an International Society of Biomechanics coordinate system convention 23 using automatic detection of bony landmarks calculated from each 3D mesh to ensure all bones were in the same orientation for measurement. Bone measurements were automatically computed using code created in python from the calculated 3D landmarks for each mesh, as described below. Bone measurements were taken from both the left and right femora/tibiae.

Angular and torsional measurements.
• Anteversion angle: angle between the neck axis of the femur (measured between a sphere fit to the femoral head and the centre of a cylinder fitted to the femoral neck), and the posterior condylar axis (measured between the medial and lateral posterior femoral condyle) ( Fig. 1) 12,24-32 . • Neck shaft angle: angle between the neck axis of the femur and the shaft axis of the femur (measured between the centre of a cylinder fit to the femoral shaft below the lower trochanter and the midpoint of the centre of a cylinder fit to each femoral condyle) ( Fig. 1) [33][34][35] . • Femoral mechanical angle (mLDFA): angle between the knee axis of the femur (measured between the most distal points on the medial and lateral femoral condyles) and the vertical y-axis (measured between the femoral head centre and the condylar midpoint) ( Fig. 1) 12,33,[36][37][38][39] . • Bicondylar angle: angle between a line perpendicular to the knee axis of the femur and the shaft axis of the femur (Fig. 1) [40][41][42] . • Tibial torsion: angle between the posterior condylar axis (measured between the medial and lateral posterior tibial condyle) and the malleolar axis (measured between the medial and lateral malleolus) (Fig. 2) 24,26,29,30,43,44 . • Tibial mechanical angle (mMPTA): angle between the knee axis of the tibia (measured between the centres of a cylinder fit to the medial and lateral tibial condyle) and the y-axis (measured between the midpoint of a cylinder fit to the medial and lateral tibial condyle and the midpoint between the medial and lateral malleolus) ( Fig. 2) 12,33,36,38 . • Rotational profile angle: tibial torsion minus anteversion angle.
Geometric fitting of a sphere to the femoral head was performed using the fitSphereAnalytic function found in the opensource python library GIAS3 (https:// github. com/ muscu loske letal/ gias3). Geometric fitting of a cylinder to the femoral neck was performed using the python library cylinder_fitting (https:// pypi. org/ proje ct/ cylin der_ fitti ng/# descr iption). This was performed by manual selection of nodes from only the template mesh for the femoral head and neck to form a point cloud for geometric fitting. Fitting a sphere to the femoral head is www.nature.com/scientificreports/ a common method for accurate determination of the femoral head centre 28,45,46 . Cylinder fitting of the femoral neck is less common as often 3d geometry is not used for measurement, however this was determined to be the best approach from both manual inspection of the proximal femoral axis and existing literature 47,48 .
Linear measurements. Computed linear measurements included Anterior Superior Iliac Spine (ASIS) width, Posterior Superior Iliac Spine (PSIS) width, pelvis depth, hip joint centre distance, femoral head diameter, femoral length, epicondylar width, condylar width, tibial length, and malleolar width (Fig. 3). Linear bone measurements were taken from automatically determined bony landmarks for each bone. The femoral length was determined by the distance between the greater trochanter and the lateral epicondyle bony landmarks. The tibial length was determined by the distance between the lateral condyle and the lateral malleolus of the tibia.

Statistical analysis.
Bone measurement results were grouped by sex and viewed in age and height groups.
Age was recorded by the VIFM in years and height was measured manually using a tape measure for each participant. We also compared epicondylar width vs. femoral length, and condylar and malleolar width vs. tibial length. www.nature.com/scientificreports/ A linear regression analysis was performed to analyse the strength of the relationship between the response (bone measurements) and the explanatory variables (age/height). A two-way ANOVA was used to determine the influence of age/height and sex on each measurement and sex differences for each age/height category.  www.nature.com/scientificreports/

Results
All measurement results and demographics are available to the public on the opensource platform SimTK.org (https:// simtk. org/ proje cts/ paed_ ssm). Sex differences in the results are only reported if the differences between groups reached a p value of < 0.05 when tested with a two-way ANOVA.
Torsional measurements. Anteversion angle showed a weak decreasing relationship with age (R = − 0.4, p < 0.001) and height (R = − 0.42, p < 0.001) from an average of 22.0° ± 9.2° at 4 years of age to 8.8° ± 8.6° at 18 years (Fig. 4). Differences between males and females were found at 15 years and 17 years of age (p < 0.001) with females having a higher mean anteversion angle than males in these groups. Tibial torsion showed a weak increasing relationship with age (R = 0.36, p < 0.001) and height (R = 0.36, p < 0.001) from an average of 32.0° ± 10.1° at 4 years to 41.1° ± 8.5° at 18 years with sex differences between 155 and 159 cm in height (Fig. 5).   Figure S3A,B). PSIS width increased from an average of 6.1 ± 0.5 cm at 4 years to 9.2 ± 0.9 cm at 18 years with a distinction between males and females as age/height increases (Fig. 7A,B). Females had a larger PSIS width than males of the same age/height with differences from 18 years/160 cm (p < 0.05) (Table S1). Pelvis depth ( Figure S3C,D) increased from an average of 7.5 ± 0.6 cm at 4 years to 14.2 ± 0.9 cm at 18 years with sex differences between the heights of 155-169 cm (p < 0.05) where females had a larger pelvis depth than males of the same height (Table S1). Hip joint diameter ( Figure S3E,F) increased from an average of 4.2 ± 0.3 cm at 4 years to 6.6 ± 0.3 cm at 18 years with sex differences at 15 years (p = 0.03) where males had a larger hip joint diameter (Table S1). Hip joint centre distance increased  www.nature.com/scientificreports/ from an average of 8.6 ± 0.5 cm at 4 years to 13.8 ± 0.7 cm at 18 years ( Figure S3G,H) with differences between males and females between 160 and 164 cm (p < 0.05) with females having a larger hip joint centre distance than males in this height range (Table S1).
Femur. Femoral length, epicondylar width, and femoral head diameter showed an increasing relationship with age (R = 0.91, 0.84, and 0.89 respectively; p < 0.001) and height (R = 0.98, 0.94, and 0.96 respectively; p < 0.001) (Fig. 8C). Epicondylar width increased from an average of 5.2 ± 0.4 cm at 4 years to 8.1 ± 0.6 cm at 18 years (Fig. 8A,B). Femoral head diameter increased from an average of 2.7 ± 0.2 cm at 4 years to 4.5 ± 0.3 cm at 18 years ( Figure S1E,F). Femoral length increased from an average of 22.6 ± 1.8 cm at 4 years to 40.3 ± 2.2 cm at 18 years ( Figure S1G,H). These measurements all showed sex differences from age 14 onwards (p < 0.05) with males having larger linear measurements compared to females of the same age/height (Table S1). Interesting to note is the divergence in the epicondylar width of males and females after the age of 13. The epicondylar width in females remained static after age 13 but continued to increase in males up until the age of 15 (Fig. 8A). Epicondylar width showed sex differences between 115-119 cm and 150-174 cm in height (p < 0.05). When comparing epicondylar width to femoral length ( Figure S4) sex differences were seen between femoral lengths 28-29 cm, and 38-45 cm (p < 0.05), with females having a smaller epicondylar width compared to males for the same femoral length.
Tibia/fibula. Tibial length, condylar width, and malleolar width showed increasing relationships with age (R = 0.89, 0.87, and 0.83 respectively; p < 0.001) and height (R = 0.98, 0.96, and 0.94 respectively; p < 0.001) (Fig. 9C). Malleolar width increased from an average of 4.1 ± 0.4 cm at 4 years to 6.5 ± 0.4 cm at 18 years (Fig. 9A,B). Condylar width increased from an average of 4.2 ± 0.4 cm at 4 years to 7.5 ± 0.5 cm at 18 years ( Figure S2C,D). Tibial length increased from an average of 20.1 ± 2.0 cm at 4 years to 36.2 ± 2.4 cm at 18 years www.nature.com/scientificreports/ ( Figure S2E,F). Sex differences were observed in these measurements from age 14 onwards (p < 0.05) with males having larger linear measurements compared to females of the same age/height (Table S1). Condylar width showed sex differences from 165 cm in height (p < 0.05). Malleolar width showed sex differences between 150 and 159 cm in height from 165 cm (p < 0.05) (Table S1), with males having larger condylar and malleolar widths compared to females in these height groups. Similar to the femur, we found a distinction between males and females from around the age of 13; small change in condylar and malleolar width was seen in females but males exhibited increased joint width until 15 years old (Fig. 9A, Fig. S2C). When comparing condylar and malleolar width to tibial length ( Figure S5) sex differences were seen from a tibial length of 36 cm between males and females (p < 0.05), with females having smaller joint widths in both cases for the same tibial length.

Discussion
The objectives of our study were to: (1) develop a consistent method for bone measurement calculation from 3D bone geometry, and (2) analyse age and sex differences in bone measurements and understand at which age these differences occur. A method for automatically and reliably computing bone measurements for the pelvis, femora, and tibiae/fibulae was developed and applied to a dataset of 333 children aged 4-18 years. Clinical bone measurements were extracted across the population and statistical analysis was performed. Key findings were: (1) the torsional profile of the femur did not vary with sex, except at the ages 15 and 17 years; (2) the torsional profile of the tibia was not influenced by sex; (3) angular measurements of the femur (neck shaft angle, bicondylar angle and mLDFA) and tibia (mMPTA) did not reveal any sex differences with age or height; (4) sex differences were observed in the linear measurements of the pelvis (PSIS width and hip joint diameter), femora (femoral head diameter, epicondylar width and femoral length) and tibiae (condylar and malleolar width and tibial length). www.nature.com/scientificreports/ Torsional measures. Reported torsional bone measurements for the femur and tibia/fibula vary widely in the literature. This is likely due to different methods of data collection (clinical or radiographic) and measurement protocols 5,19,49 . For femoral anteversion, these measures include using clinical tests such as maximum lateral trochanteric prominence related to the degree of internal rotation of the hip in prone, X-rays, MRI, or CT 11,49 . For tibial torsion, equivalent measures are transmalleolar axis, CT, and MRI 50 . To the authors knowledge, there are no existing studies which have calculated torsional measures for both femur and tibia from 3D bone geometry in children.
In the current study, the femoral anteversion angle decreased with age from an average of 22° at 4 years to 9° at 18 years over the dataset. Sex differences were only found for femoral anteversion at ages 15 and 17 years, consistent with previous adult studies, showing that females have a larger anteversion angle by about 5°1 2,25,29 . Greater change occurred in first 8-10 years of life, with smaller changes after that age continuing up to age 18 years. This decrease over time is also consistent with previous studies, with femoral anteversion for TD children reported to decrease on average from 40° at birth, to 24° at 10 years, 20° by mid to late adolescence and 16° in adulthood 5,10,30,[51][52][53][54][55] . It is important to bear in mind that multiple methods to measure femoral anteversion exist. These result in 16°-20° differences across the full range of anteversion for the same participant resulting in reported anteversion angles for adults between 7° and 24°5 , 49 . This study showed decreasing femoral anteversion with age, greatest in the first 8-10 years, but continuing into (and past) skeletal maturity. These findings support other studies which suggest that femoral anteversion may continue to slowly decrease into adulthood 5 , for reasons not well explained.
This study also showed a gradual increase in external tibial torsion with age from about 32° to 41°. This is consistent with existing studies which found increasing tibial torsion from 27° to 35° from 6 to 30 years of age 56 and from 34° to 36° in a 3 to 10 year age group 57 . However, the range of reported tibial torsion varies greatly www.nature.com/scientificreports/ and only a few studies have investigated children. The measurements from the current study on 3-D CT were slightly more lateral (external) than the reported clinical measures. CT measures of tibial torsion define rotation between the proximal and distal ends of the tibia. However, clinical measures assess tibial rotation relative to a flexed knee position, which induces some medial rotation of the tibia 58 . As a result, CT measures of tibial torsion can be more lateral than clinical measures 50 but likely reflect true bony torsion. Sex differences for tibial torsion were only observed between 155 and 159 cm in height, consistent with the adult literature stating no sex differences in the adult population 56 . This study demonstrated the wide range of anteversion angle and tibial torsion that can be considered as normal in a paediatric population. Although sex differences are minimal, the anteversion and tibial torsion angles have been shown to moderately decrease and increase respectively with age with an overall increasing torsional profile during growth. Angular measurements. Angular measurements showed small variation with age and height and few sex differences. Neck shaft angle decreased with age from an average of about 139° to about 132°, which is consistent with previous studies where femoral neck shaft angle has been shown to generally decrease from childhood to adulthood 59 (from ~ 150° at birth to ~ 140° aged nine years, to ~ 128° in adulthood 3,10,53,59,60 ). mLDFA on average was between 84° and 87° in this study, which is slightly lower than a previous study which found mLDFA values of 87°-88° in children aged 4-18 years 13 and adult values ranging from 87° to 91°1 2,37,38 . However, few studies have reported this angle in a paediatric population. mMPTA on average was between 86° and 90°. This is consistent with a previous study which found mMPTA values of 88°-90° in children aged 4-18 years 13 and adult values ranging from 82° to 88°1 2,37,38 .
No sex differences were found for the neck shaft angle and mLDFA in this dataset, however, differences have been reported in adult studies 12,25,38,59 . For example, neck shaft angle was found to be higher and mLDFA to be lower in females by 1°-2°1 2,25,38,59 . These sex differences may take longer to develop in the lower limb bones once the bone has stopped growing and is modelled based on loads experienced. mMPTA showed sex differences only at 17 years of age, which is supported by previous studies in adults with females showing 1°-2° higher mMPTA [37][38][39] .
Overall femoral and tibial angular measurements do not appear to be influenced by sex and age/height. Worth noting is the large standard deviation in any angular measurements for a given age/height, which highlights the variability of these measurements in a typically developed population.
Linear measurements. Pelvic, femoral, and tibial linear measurements increased with age and height as was expected and sex differences were observed for many of the measurements. The sexual dimorphism in the pelvis is of interest in the field of obstetrics. In this study, the most marked sex difference was in the PSIS width with an increase in PSIS width in females at 18 years old and from 160 cm in height, which is consistent with the shape differences found between the adult female and male pelvis 15 and the posterior space being more influenced by sex 61 . Sex differences were seen in the hip joint centre distance between 155 and 164 cm in height which is also consistent with literature 62 .
For all linear measurements of the femur and tibia/fibula, sex differences were seen beyond 13 years old and at various height ranges. When comparing to bone length, the epicondylar width showed sex differences from a femoral length of 38 cm onward, with females having smaller epicondylar width compared to males for the same femoral length. Similarly for the tibia/fibula, sex differences were observed from a tibial length of 36 cm onward with condylar and malleolar width being smaller in females compared to males for a similar bone length. This is consistent with prior literature comparing the adult knee between females and males 14,17,18 and highlights the importance of patient-specific treatment protocols such as orthopaedic implant size selection and sports injury prevention.
Limitations. This study has several limitations to be considered when interpreting the results. First, the dataset was obtained from a subset of the population living in the state of Victoria in Australia with 75% of the population living in an urbanised area which would be similar to most developed countries but could be different from groups living in more rural areas. While ethnicity was not recorded for this data, the top five ethnicities recorded in the state of Victoria are English (24%), Australian (22%), Irish (8%), Scottish (7%), and Chinese (5%) (Australian census, 2021). Both factors could potentially impact measurements and the applicability of these findings to other populations. Additionally, some age groups had fewer number of CT scans (Table 1) meaning the population in these age groups may not be fully represented. The sex distribution is also not equal for some of the age/height groups therefore caution is advised when interpreting sex differences in these groups. As the data was de-identified, we had access to participant age in years (not months) at the time of the CT scan. Therefore, a child referenced as 4 years old may be 4 years and 1 month old or 4 years and 11 months old, during which time large growth changes may occur. Therefore, we also examined these measurement changes with height. Also, inferences regarding morphological bone changes due to growth should be made with caution, as these data are cross-sectional, rather than longitudinal. Cadaveric stature was measured in this study rather than standing/ living stature which may result in differences in participant height. When conducting the statistical analysis, both left and right bone measurements were used for the femora and tibiae/fibulae, we acknowledge that there is some variation in limb length for an individual and that it is less than the variation between individuals. This may affect the averages presented for each age/height grouping.
To use the automated bone measurement methods developed in this study, three-dimensional bone surfaces reconstructed from full lower limb CT or MRI scans are required. This limits the application of our method, however, we have also developed statistical shape models that can be used to predict the bone morphology from www.nature.com/scientificreports/ sparse anatomical landmarks 20 . Future integration of these methods will enable clinicians to compare patientspecific data to our population norms.

Conclusions
We developed an automated workflow to compute lower limb bone measurements and rotational profiles in children aged 4-18 years. We found sex differences in the linear bone measurements in the pelvis, femur, and tibia/fibula beyond the age of 13 years. This rich dataset can be used as an atlas for researchers and clinicians to understand typical development of critical rotational profiles and linear bone measurements in children. Finally, all computed bone measurements and code for automatically extracting bone measurements from 3D point clouds is available on the opensource platform SimTK.org (https:// simtk. org/ proje cts/ paed_ ssm).

Data availability
All data generated or analysed during this study are included in this published article and its supplementary information files. Raw data is available to the public at the following link: https:// simtk. org/ proje cts/ paed_ ssm. www.nature.com/scientificreports/